The in-game options menu recommends controller, and the optimization for KB/M could have been much more intuitive (no mouse controls on menus -- boo), but the control scheme is pretty simple. Just left/right character movement, left/right level rotation, an action button for activating the inversion spots, and a button to reverse time. You should be fine with just keyboard, if that suits you.

Honestly, nothing feels right... the controller triggers don't spin the world fast enough for my tastes - maybe it's to prevent unwanted physics? I'd be interested in trying the game on a platform with an accelerometer, but it feels too slow-paced to keep my attention as is.

The in-game options menu recommends controller, and the optimization for KB/M could have been much more intuitive (no mouse controls on menus -- boo)

This was actually a conscious design choice. Since the entire game is controlled via keyboard, it wouldn't make sense to need to jump to a different device (Mouse) just for menu navigation. It feels kinda awkward since we're all pretty used to navigating menus with a mouse, but the concept makes perfect sense.